Question

Need some help I do not necessary want the answer but the process to get the answer, thank you.

Answer 1

Given function :$f(x) = 2x^3 + x^2-3x + 1$.

We need to find the average rate of change from x = −2 to x = 0.

Let us find the values of y-coordinates for x=-2 and x=0 for the given function on the graph.

$f(-2) = 2(-2)^3 +(-2)^2-3(-2) + 1=-5$

$f(0)=\:2\left(0\right)^3\:+\left(0\right)^2-3\left(0\right)\:+\:1 =1$

Formula for average rate of change is :

$f_{avg}=\frac{f(b)-f(a)}{b-a}$

Plugging the values of f(a), f(b), a and b in the above formula, we get

$f_{avg}=\frac{0-(-5)}{0-(-2)} = \frac{5}{2}$.

Therefore, the average rate of change from x = −2 to x = 0 is $\frac{5}{2}$.